Investigations On The Electromagnetic-thermoelastic Problems With Temperature-dependent Properties In Nonlocal Temporal Or Spatial Scale

In classical heat transfer theory,the heat conduction equation is diffusional,which predicts an infinite speed for heat transfer in the medium.Physically,this is not true and is opposite to the experiment observation.Therefore,to eliminate such defect and depict the heat wave effect,the non-Fourier's heat conduction laws have been proposed in succession.To describe the coupling effect between deformation field and temperature field,scholars developed the generalized thermoelasticity theory based on the above the non-Fourier's heat conduction laws.The fractional calculus theory can make up for the deficiency of integral calculus theory.With the successful application of fractional calculus in heat conduction,anomalous diffusion and viscoelasticity,scholars have extended fractional derivative to generalized thermoelasticity theory and developed fractional integral generalized thermoelasticity theory.Based on the memory dependent properties of memory dependent differential derived by fractional derivative,scholars have established fractional differential generalized thermoelasticity theory.The development of above generalized thermoelastic theory is only taking the time microscale into modifying the heat conduction equation,and its elastic control equation is remain classical and only applicable to material or structure of relatively large size or scales.However,the classical elastic equation may fail as the external characteristic length of the medium approaches to the internal characteristic length.In order to make up for the deficiency of classical elasticity theory,scholars have modified the classical elasticity theory and obtained the nonlocal elasticity theory that can describe the size dependent effect.In present work,based on the L-S generalized thermoelastic theory and nonlocal elastic theory and memory dependent differential,the generalized electromagnetic-thermoelastic coupling problem of a rod and hollow cylinder is analyzed by means of Laplace transform and its inverse transform technology.The specific contents are as follows:(1)Based on the L-S generalized thermoelasticity and nonlocal elasticity theory,the dynamic response of a finite elastic rod fixed at both ends subjected to a moving heat source is investigated.The effects of the velocity of the heat source,the nonlocal parameter and the variables properties on non-dimensional stress,temperature and displacement are investigated.The results show that the velocity of the heat source and the variables properties markedly influences the variations of the considered variables,while the nonlocal parameters barely influences the variations of the non-dimensional temperature,and slightly influences the nondimensionless displacement and significantly influences the variations of the peak value of the non-dimensional dimensionless stress(2)In the context of the theory of memory-dependent generalized thermoelasticity,the dynamic response of a hollow cylinder the inner surface is subjected to thermal shock is investigated.The results show that the nonlinear kernel function reflects the heat propagation velocity smaller than the linear kernel function.Moreover,the time-delay factor can be used as a new parameter to predict different results,and it has a more obviously influences under the improved kernel function.The variables properties markedly influences the peak value of the considered variables.